Apple stays true to Steve Jobs’ maxim that users don’t want to subscribe to music, but Rhapsody hopes the company will allow its “rental” service to fill that niche on the iPhone — despite a history of animosity between the two companies. Rhapsody’s yet-to-be-approved app for the iPhone and iPod Touch would allow Rhapsody subscribers to stream more than 8 million tracks, including all their existing playlists and customized collection.

If you already pay $15/month for Rhapsody To Go (the same option that allows playback on devices that support Microsoft’s PlaysforSure DRM), Rhapsody for the iPhone would be free to download and use. That’s the good news.

Now for the bad news: Rhapsody told Wired.com that the app will operate on either 3G or Wi-Fi, but lacks an offline playback mode, unlike Spotify’s app, submitted earlier. That means that without a solid 3G or Wi-Fi connection, the iPhone app will not play music. For a service like this to be a reliable mobile listening option, an offline mode is of the utmost importance. Otherwise, the app is more a novelty — if you can’t listen to it on the subway or the highway it’s not your primary portable music player.

Rhapsody confirmed what it told gdgt — that it plans to try to add an offline mode in the next generation, but only if Apple allows this version of the app into the store. Rhapsody has also made another concession to Apple: If a user decides to buy a track while streaming it, the “buy” links go to iTunes’ AAC store, rather than to Rhapsody’s MP3 store.

Spotify’s iPhone app, on the other hand, includes no “buy” links to iTunes. That’s something Apple could view as a slap in the face, along with the offline mode that would obviate the need for some users to purchase music at all, let alone purchase it from iTunes. Apple could block Spotify’s iPhone app (possibly driving its users to the Android platform), while approving Rhapsody’s app.

These two old digital music foes could find it in their best interest to forge an alliance when faced with the game-changing nature of Spotify and other cloud-based music services.